If you connect your router to the cable modem, and then connect via an ethernet cable from the router to your laptop/PC then run your test.
This will tell you if your router is able to keep up with the speed of your cable modem.
If you find out it's your wireless that's slowing you down (which I'd bet it is, then invest in a new router, and do some research on the model you're looking at before you jump the gun and purchase it. read the reviews, look at the tests performed on them.
FYI - Linksys was sold to belkin a couple of years ago - so just be aware the brand name may not carry the same performance and reliability of years gone past.